1. insert a rational number and an irrational numbers between a)0.1 and 0.11

For this case we have the following definition:
 A real number can be a rational number or an irrational number.
 The rational numbers are those that can be expressed as the quotient of two integers, such as 3/4, -21/3, 5, 0, 1/2, while the irrational numbers are all the others.
 Between 0.1 and 0.11 we have:
 Rational number: 105/1000 = 0.105
 Irrational number: 01057685429832687